Question 14

NUMERICALHARD

In the following reaction sequence, major products X and Y are acyclic monomers.

CH3I→1. KCN2. H3O+,Δ3. Red P, Br24. NH3 (excess)XCH_3I \xrightarrow{\substack{1.\text{ KCN} \\ 2.\text{ H}_3\text{O}^+, \Delta \\ 3.\text{ Red P, Br}_2 \\ 4.\text{ NH}_3 \text{ (excess)}}} X

Caprolactam→ΔH3O+Y\text{Caprolactam} \xrightarrow[\Delta]{H_3O^+} Y

500500 mol of X completely reacts with 500500 mol of Y to give 11 mol of a single biodegradable acyclic copolymer Z as the only product. The amount of Z formed in grams is ____.

Given: Atomic mass (in amu): H : 1, C : 12, N : 14, O : 16, Br : 80

Correct Answer: 85018

Detailed Solution

  1. Identify X: CH3I→KCNCH3CN→H3O+CH3COOH→P,Br2BrCH2COOH→NH3NH2CH2COOHCH_3I \xrightarrow{KCN} CH_3CN \xrightarrow{H_3O^+} CH_3COOH \xrightarrow{P, Br_2} BrCH_2COOH \xrightarrow{NH_3} NH_2CH_2COOH (Glycine).

    Molar mass of Glycine (C2H5NO2C_2H_5NO_2) = 2(12)+5(1)+14+32=752(12) + 5(1) + 14 + 32 = 75 g/mol.

  2. Identify Y: Hydrolysis of caprolactam yields Ο΅\epsilon-aminocaproic acid (NH2(CH2)5COOHNH_2(CH_2)_5COOH).

    Molar mass (C6H13NO2C_6H_{13}NO_2) = 6(12)+13(1)+14+32=1316(12) + 13(1) + 14 + 32 = 131 g/mol.

  3. Formation of Z: 500500 mol X + 500500 mol Y reacts to form 11 mol of copolymer Z (Nylon-2-nylon-6). Total monomers = 500+500=1000500 + 500 = 1000. Number of peptide bonds in a single acyclic chain of 10001000 units = 1000βˆ’1=9991000 - 1 = 999.

    Each bond formation releases one H2OH_2O molecule (1818 g/mol).

  4. Calculation: Mass of 11 mol Z = (Total mass of reactants) - (Total mass of water lost)

    Mass = (500Γ—75)+(500Γ—131)βˆ’(999Γ—18)(500 \times 75) + (500 \times 131) - (999 \times 18)

    Mass = 37500+65500βˆ’17982=103000βˆ’17982=8501837500 + 65500 - 17982 = 103000 - 17982 = 85018 g.

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